Ratio of amplitude for two wave is 5:10 .Find the ratio of intensity?

Explanation

To find the ratio of intensity for two waves given the ratio of their amplitudes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
The ratio of amplitudes of the two waves is given as:
\[ \frac{A_1}{A_2} = \frac{5}{10} \]

2. **Understand the Relationship Between Intensity and Amplitude:**
Intensity (\(I\)) is directly proportional to the square of the amplitude (\(A\)). This can be expressed mathematically as:
\[ I \propto A^2 \]
Therefore, the ratio of intensities can be expressed in terms of the ratio of amplitudes:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

3. **Substitute the Given Ratio of Amplitudes:**
Substitute the ratio of amplitudes into the equation:
\[ \frac{I_1}{I_2} = \left(\frac{5}{10}\right)^2 \]

4. **Calculate the Square of the Ratio:**
Calculate the square of \(\frac{5}{10}\):
\[ \frac{I_1}{I_2} = \left(\frac{5}{10}\right)^2 = \frac{25}{100} \]

5. **Simplify the Ratio:**
Simplify the fraction:
\[ \frac{I_1}{I_2} = \frac{25}{100} = \frac{1}{4} \]

### Final Answer:
The ratio of intensity \(I_1 : I_2\) is:
\[ 1 : 4 \]